Heat engines

ABSTRACT

There is provided a gas cycle which is of particular usefulness in the utilization of heat which is not of relatively high temperature. An engine operating with the subject gas cycle may use thermal energy derived from Radioisotope decay.

United States Patent Rao June 6, 1972 [54] HEAT ENGINES [72] Inventor: Venkataramanayya K. Rao', Bangalore, [561 References cited lnda UNlTED STATES PATENTS [73] Assignee: Atomic Energy of Canada Limited Commerits. Ottawa Ontario, 2,869,830 l/ I959 Cox ..60/59 T Canada Primary Examiner-Martin P. Schwadron [22] Filed: Nov. 21, 1969 Assistant Examiner-Allen M. Ostrager [21 1 pp No: 878,817 Attomey-Cushman. Derby & Cushman [57] ABSTRACT F A ti Pri I Data [30] onign ppnca on on y There is provided a gas cycle which is of particular usefulness Feb. 14, 1969 Canada "042,928 in the utilization of heat which is not of elatively emperature. An engine operating with'the subject gas cycle may [52] LS. Cl ..60/24, 60/36, 60/59 T se thermal energy derived from Radioisotope decay 7/06 Field of Search ..60/24, 25, 36, DIG. 4, 59 T 7 Claim, 11 Drawing Figures COOLER E HEAT SOURCE PATENTED I 6:912 3,667,215

SHEET 10F 8 [SETOPE SOURCE THERMAL EFFICIENCY PRESSURE RATIO FIG. 1

PRIOR ART MZVM @404 XWZVM PATENTEDJUH 6 I972 3,667, 215

SHEET 20F s 2 9 l8- 2 t I? MAX CYCLE TEMP= |570R(600) uJ EQUAL ENTHALPY DROPS THROUGH T. aIT

E g A B 5 l5 ISENTROPIC EFFICIENCY OF COMPRESSOR e0 70 E ISENTROPIC EFFICIENCY OF TURBINES a5 75 I4 EXCHANGER EFFECTIVENESS so 75 A B Io PRESSURE RATIO PRIOR ART' FIG. 2 //V///V7"0A VZ/v/mm/Ffi/w/vm w 9/90 ZMZWM JMQVZMZMVE PATENTEDJUN 6 I972 3 667. 215

SHEET 30F 8 HEAT SOURCE GENERATOR 4 COOLER CONDENSER FIG. 3

PRIOR ART T T T a /W I I I) 1 J Z Z J s s s WET EXPANSION DRY EXPANSION IDEAL EXPANSION FlG. 4A FIG. 4B FIG.4C PRIOR ART PRIOR ART PRIOR ART PATENTEDJUH 6 m2 3, 667, 215

HEAT SOURCE Q3 7 V4 J COOLER FIG. 5

A77 in/5y;

P'A'TENTEnJun 6 I972 SHEET 5 BF 8 mUmDOm .ZmI

A BEGENERAIQB COOLER PATENTEnJuu 6 I972 3, 667. 215

sum sur 8 Ideal Thermodynamic Cycle of Engine of Invention Adlabatic Compression Constant Pressure Heat Addition In Regeneration Constant Volume Heat Addition In Heat Source Adiabatic Expansion Constant Pressure Heat Rejection In Regenerator Constant Pressure Heat Rejection In Cooler (Heat Sink) /MM M J XM A 770 fi/VE y;

PI-IIEIITEIIJUII 6 I972 3 667. 215

SHEEI 70F 8 WORKING MEDIUMICARBON DIOXIDE SP OUTPUT WATTS LBM PER SEC THERMAL EFFICIENCY T4= I540R I0- W V L l J I J o 2 4 e 8 IO COMPRESSION RATIO A THERMAL EFFICIENCY WITH REGENERATION B THERMAL EFFICIENCYNVITHOUTREGENERATION C SPECIFIC OUTPUTI WATTS ILBM PER SEC FIG. 8

By AA N W WZWE PAIENTEIIIIIII 8|972 3,667,215

SHEET 8 0F 8 WORKING MEDIUMI AIR SP OUTPUT WATTS/LEM PER SEC THERMAL EFFICIENCY l T=l570R 2 4 20,000- 20- I T 54OR I 6 5 I0- v o 2 4 s a COMPRESSION RATIO AZ THERMAL EFFICIENCY WITH REGENERATION B I THERMAL EFFICIENCY WITHOUT REGENERATION I C ISPECIFIC OUTPUT: WATTS/LEM PER SEC FIG.9

zwzm; W4C, v MAWE HEAT ENGINES This invention relates to a method and apparatus for the I thermal to mechanical conversion of energy. The invention has particular, but not exclusive application, in the ufilization of heat which is not at a relatively high temperature.

The present invention resulted from a need to provide a small heat engine to convert thermal energy, derived from decay of a radioisotope source, into mechanical and electrical energy. Such a requirement was stimulated in the expectation that certain navigational aids, i.e. lamps, fog detectors, fog signals, radio beacons etc., could be left unattended for long periods in remote locations.

In order to obtain reliability, safety, and maximum utilization of relatively expensive radioisotope sources, it was envisaged that the minimum efficiency of conversion be set at 20 percent, that the power output for one embodiment be of the order of 600 watts and that the maximum temperature of the available thermal energy be about 600 C.

With these objectives in view, all the methods available for energy conversion were investigated in detail. This is described below and the present invention is set forth at the end as an attractive method of energy conversion. It is to be noted, however, that the field of application of this invention is quite general and not limited only to applications such as the one stated above.

It is an object of one feature of the invention to provide a method of converting thermal to mechanical energy in a continuous closed cycle utilizing a working medium which is at all times gaseous.

In accordance with this object, the method comprises the steps: compressing a gaseous medium in a first space having a lower mean temperature and pressure by a compression ratio r," adding heat at substantially constant pressure to the compressed medium, adding further heat from a source to the compressed medium at substantially constant volume, expanding the said medium into a second space having a high mean temperature and pressure by an expansion ratio R, where R is greater than r, extracting an amount of heat from the expanded gas at substantially constant pressure and substantially equal to the first mentioned added heat, cooling said medium at substantially constant pressure, utilizing the work done by the medium during expansion to provide the work required for the compression step and a mechanical output, and, cycling repeating all the foregoing steps.

It is an object of another feature of the invention to provide apparatus for converting thermal energy to mechanical energy using a gaseous medium.

In accordance with this other object, the invention comprises: compression means for compressing the working medium by a ratio of r, heat exchanger output means for adding heat at constant pressure to the compressed medium, means for adding further heat at constant volume, expansion means a second portion of the energy converted in the expansion means to a mechanical output, and, means for respectively cycling all the foregoing means in succession.

The invention will be described with references to the accompanying drawings in which:

FIG. 1 (prior art) is a diagram of a simple gas turbine power plant and the computed thermal efficiency as a function of pressure ratio.

FIG. 2 (prior art) is a similar diagram to the preceding one, differing from it by the incorporation of reheat and regeneration into the plant.

FIG. 3 (prior art) shows the basic components of the Rankine cycle.

FIGS. 4A, 4B, 4C (prior art) are graphs of Temperature-Entropy characteristics for the Rankine cycle using Wet, Dry and Ideal Expansion, respectively.

FIG. 5 is a diagram of a heat engine, according to the present invention, on its upward stroke.

FIG. 6 is similar to FIG. 5, but wherein engine is on its downward stroke.

FIG. 7 is a Pressure-Volume diagram of the ideal thermodynamic cycle of the heat according to the present invention.

FIGS. 8 and 9 are graphs depicting the computed performance characteristics of the ideal thermodynamic cycle as in FIG. 7 with carbon dioxide and air, respectively, as working media.

Conversion of thermal to electrical energy can be accomplished in two ways:

1. Direct Conversion 2. Indirect Conversion For use with radioisotope sources, only two methods of direct conversion need be considered(a) Thermoelectric and (b) Thermionic conversion systems. Both the systems are in service and under development in great variety by a number of civil and military organizations mainly in the United States. The most recent and comprehensive source of reference of these endeavors is the Proceedings of the 1967 Intersociety Conference on Energy Conversion Engineering. Numerous power generators built under the SNAP program-Systems for Nuclear Auxiliary Poweruse one or the other of these two methods of energy conversion. The present state of the art of these devices is summed up in the table below.

Energy conversion technique Material problem.

It is unlikely that the conversion efficiency of these devices will be improved sufficiently in the near future to compare with the requirements previously discussed. In addition, research and development work in these fields would be expensive and protracted. For these reasons, the direct conversion systems can be ruled out for the present application.

The indirect conversion systems, which can also be called dynamic conversion systems, make use of a heat engine to convert thermal power to mechanical, which is later converted easily to electric power. Here, there is a choice in regard to the thermodynamic cycle on which the heat engine operates. The cycles of the dynamic conversion systems that have been constructed and that are under intensive development are the following:

a. Brayton Cycle b. Rankine Cycle c. Stirling Cycle.

Closed cycles are used exclusively as the cycle can be open only when air is used as the working medium."

Conversion systems operating on these cycles are examined next with particular reference to the present application.

BRAYTON CYCLE 1 This is the cycle on which a Gas Turbine power plant operates. The working medium is a gas which does not change phase during the cycle. Any gas may be used as the working medium as the performance of the system is, theoretically, independent of the properties of the working medium. There are no problems of degradation of the working medium due to high temperatures or irradiation.

The thermal efficiency of the Brayton Cycle depends on the maximum cycle temperature and is extremely sensitive to component performance. The basic cycle'has to be modified inorder to obtain reasonable thermal efficiencies. The modifications include regeneration and reheat.

A detailed analysis of the Brayton Cycle with difierent modifications wascarried out using a digital computer. The results of the analysis are presented in FIGS. 1 and 2.

FIG. 1 represents the performance of what is termed the CBTX cycle. A schematic layout of the system working on the CBTX cycle is shown therein. The working medium is compressed in the compressor C and heated in the heater B using the radioisotope source after passing through the regenerator X. The gas then expands through the turbine Twhich exhausts through the regenerator X. An open cycle is shown on the assumption that the working medium is air. The power available on the turbine shaft in excess of the power requirements of the compressor is the useful power.

.The following assumptions were made in deriving the results shown in FIG. 1; g

Maximum Cycle temperature=Max. temp. at the isotope source (600 C.) Sink temperature 1 50 C. v lsentropic efficiency of Compressor80 percent lsentropic efficiency of Turbine-85 percent Effectiveness of Regenerator-SO percent Pressure loss through heater-2 percent of compressor delivery pressure Pressure loss through regenerator-l psi. l The component efficiencies assumed represent the upper limit'thatcan be expected within the present state of the art in the sizes as small as are to be employed in the present application. It is seen that the maximum value of the thermal efficiency of 16.86 percent occurs at a pressure ratio of 2.6. This, when multiplied by the Generator efficiency (-85 percent) and the Mechanical efficiency (-90 percent) results in an Overall Conversion efficiency of about 13 percent.

.The efiiciency can be improved somewhat by using a more complicated system as depicted in FIG. 2 which is designated as the CBTRTX cycle. This cycle incorporates both reheat and regeneration. The working medium is re-heated back to the maximum cycle temperature after a partial expansion through the turbine T and expanded again to the lowest possible pressure through the turbine T As is evident, this is a more complicated arrangement than the previous one.

The same assumptions as for the CBTX cycle were made in deriving the results for the CBTRTX cycle shown in FIG. 2 by curve A. In addition, it was assumed that the enthalpy drops through the'two turbines T and T, were equal as this is found to give the best results. It is seen that the maximum efficiency of 26 percent occurs at a pressure ratio of 3.4. This, when multiplied by the Generator efficiency (-85 percent) and the Mechanical efficiency (=90 percent) results in an Overall Conversion efficiency of barely 20 percent.

The reason for the low efficiency is primarily the low value of-the maximum cycle temperature (600 C.) imposed in the lsentropic efficiency of turbines 75 percent Effectiveness of regenerator 75 percent All other assumptions as before.

The maximum efiiciency of 10.96 percent occurs at a pres- I sure ratio of 2.6 in this case. This extreme sensitivity of the Brayton Cycle to component performance will require a very careful matching of the various components of the system for optimum performance. This entails long and painstaking development work.

The Brayton Cycle can hence be ruled out for the present application especially in view of the merits of the other cycles to be discussed next.

RANKINE CYCLE The Rankine Cycle is inherently a very eflicient cycle because heat addition and heat rejection take place mainly at the highest and at the lowest cycle temperatures respectively. The basic components of a Rankine system are the turbine, the feed pump, the heat source and the heat sink or condenser and are shown in FIG. 3. The main feature of this system is that the working medium undergoes a phase change during the cycle.

Steam has been used as the working medium almost exclusively in Rankine cycle systems. Unfortunately, it is quite unsuitable as a working medium in small units of the size contemplated at the present. The suitability or otherwise of a fluid as the working medium of a Rankine system is decided by the way it affects the design and performance of the turbine which is the most critical component of the entire system.

The effect of the fluid properties on turbine design can be shown by using normalized design parameters as used by Balje. These are:

the Specific Speed N,=(NQ" (H and the Specific Diameter D,=(DH (Q where Q= exhaust volumetric flow D== turbine diameter H lsentropic head drop through turbine, ft.

Balje has provided contours of constant efficiency on N,D, plots. For optimum performance, then, a turbine must operate at fixed values of N, and D,. Consequently N, X D, constant for that point, so that (N-D) (HQ constant. This shows that the turbine tip speed is directly proportional to the square root of the enthalpy drop through the turbine.

From both mechanical and aerodynamic considerations, it is desirable to keep the tip speed of the turbine low. This then requires a low enthalpy drop of the working medium between the source and sink temperatures. It is here that the fluid properties bear their influence.

The three significant properties of the fluid that have an important bearing on turbine design and performance are:

1. The critical pressure 2. The molecular weight, and

3. The quality of the vapor after it undergoes an isentropic expansion from a saturated state; i.e., whether it becomes wet or superheated" after expansion.

The influence of the critical pressure of the fluid is seen from the following approximate argument:

The expansion through the turbine is, ideally, isentropic. The source and sink temperatures and the mean pressure level in the system are assumed fixed.

We have:

Z (ompresslblhty Facto RT from which we get:

((1 ln Z) r) In Tr I'r In the above relations;

Vr=Relative Volume=Vl Vc where Vc=Critical Volume Tr=Relative Temperature=T/ Tc where Tt=Critical Temperature Pr=Relative PressurFP/Pc where Pc=Critical Pressure Cp=Specific Heat at constant pressure. From the tables listing the properties of corresponding states (variation of 2 with Prand Tr), we see that the L.H.S. of equation (2) increases with an increase in Pr. In other words,

decreases as Pr increases. This indicates that a low critical pressure of the working fluid is' desirable.

The influence of the molecular weight of the fluid is seen by the following argument: The energy in a unit mass of vapor expanding between two fixed temperatures is approximately inversely proportional to its molecular weight since enthalpy drop Cp( T,T

The speed of the turbine therefore decreases with an increase in the molecular weight of the fluid. Since a definite volume flow is to be maintained for a given output, the components of the turbine can be made larger and more efiicient in low power units.

The other property of the fluid of significance in turbine design is the slope of the saturated vapor line on Temperature- Entropy coordinates. If this slope is negative, as is the case with water and liquid metals, the vapor becomes "wet after expansion through the turbine nozzle giving rise to erosion problems. If the slope is positive as with many organic fluids, the vapor becomes superheated after expansion and needs to be de-superheated before it can be condensed. The ideal situation, of course, is to have an infinite slope for the line. These three cases are shown in FIG. 4.

These considerations indicate that it is desirable to use a fluid having a low critical pressure and a high molecular weight, particularly in the very small sizes of turbine contemplated. Thus steam is unsuitable on both these counts.

Much work has been done on the use of Mercury as a working medium for small Rankine cycle power systems. The advantage of its high molecular Weight (200) seems to be more than ofi'set by its high critical pressure (200 atm). Mercury has also a wet" expansion. It has, in addition, many attendant difficulties concerning the mechanical design of the turbine components. These arise mainly because of the difi'lculty of lubricating the bearings with Mercury and because of the extreme corrosiveness of Mercury especially when both liquid and vapor are present. The SNAP 1 power system which used Mercury as the working fluid had the following performance characteristics:

Electrical Power Output 500 watts at 1 15 volts.

Turbine Inlet Temperature 704 C.

Condenser Temperature 167 C.

Turbine Speed 40,000 rpm.

Turbine Isentropic Efiiciency 46% Alternator Efiiciency 86% System Overall Efficiency 9.4%

Operational Life 104 days.

Another small Rankine cycle power system with Mercury as the Working fluid is under active development by the Junkers Flugzeug und Motorenwerke AG, of Germany.

From the point of view of every consideration listed above, many organic fluids appear very attractive as working fluids for small Rankine cycle power systems. Monochlorobenzene, Dichlorobenzene, FC-75 etc. are typical examples of such fluids. In general, these fluids have a low critical pressure, a high molecular weight and a dry expansion vapor line. Their thermodynamic properties, thermal and irradiation stabilities are not yet fully investigated. Nevertheless, there is little doubt that they are ideally suited for applications such as the present.

Small Rankine cycle power systems ranging in power from 200 to 800 watts, that use organic working fluids have been marketed. These have been used predominantly with solar energy sources. The typical performance of such a 400 We unit is as follows:

Boiler temperature 120 C.

Condensing temperature 55 C.

Brake Thermal Efficiency= 10%.

. Generator efficiency= 75%.

Overall Efficiency 6%.

The adaptation of such a unit for the present application might be the subject for a development study. One obvious problem is the thermal stability of organic working fluids at higher temperatures.

STIRLING CYCLE Though the conception of the Stirling Cycle dates back to 1816, the successful evolution of a heat engine operating on the cycle has been accomplished only recently.

The Stirling Cycle is a regenerative cycle and, theoretically, achieves the highest possible thermal efficiency between a given set of source and sink temperatures. The thermal efficiency of the Stirling Cycle is the same as that of the Carnot Cycle. The evolution of a mechanical device to operate on this thermodynamic cycle has needed very ingenious and refined mechanical design. The Philips engine is a very elaborate mechanical arrangement with two coaxial pistons reciprocating in one cylinder with no lubrication. The working medium is either Helium or Hydrogen gas at a mean pressure of about 1 1O atmospheres. These high mean pressures are required to achieve a reasonably high specific output (output/weight) from the engine and naturally impose problems of the dynamic seal between the piston rod and the cylinder. The maximum source temperature is at present limited to 700 C. It is contemplated that this will be increased to 800 C. and the mean gas pressure to 220 atmospheres with the use of better creep resisting materials in the near future.

The performance figures quoted for a commercially available engine are very impressive indeed. They are:

Source Temperature 700 C.

Sink Temperature 25 C.

Brake Thermal Efi'iciency= 41%.

Overall Efiiciency including Electric Generator The Carnot Efficiency for these temperature levels is 69.4%. This shows that this engine achieves a Relative Efficiency (Actual Efficiency/Ideal Efficiency) of nearly 60%.

The adaptation of the Stirling Engine to an isotope source might be a proposal for future developments, but licence cost, reliability and materials are all real problems.

THE PRESENT INVENTION A simple mechanical device intended to work on a new thermodynamic cycle of high efficiency which may be adapted to a radioisotope source will now be presented. Though this thermodynamic cycle is not as efficient as the Stirling Cycle, it is more efiicient than most conventional cycles. The simplicity of the corresponding mechanical device might make the concept of this heat engine worth pursuing further.

The engine consists of a mechanism containing a cylinder and reciprocating piston in which both sides of the piston are utilized to subject a working medium to various thermodynamic processes. Some of these processes occur simultaneously above and below the piston. A heat source, a heat sink and a regenerator are the other components of the engine. Valves are located in the passages connecting these components with each other to regulate the flow of the working medium among them.

The working of the engine will be described with reference to the diagramtic sketches shown in FIGS. and 6. 7

FIG. 5 shows the piston in its upward stroke. During this stroke, the following events take place:

a. in the space above the-piston: Valve V is closed. Valve V, is open. Hot gas is displaced into the Cooler (Heat sink) through the Regenerator.

- b. in the space below the piston: Valve V is open. Valve V is closed. Cool gas from the Cooler is sucked in.

FIG. 6 shows the piston in its downward stroke. During this stroke, the following events occur:

a. in the space above the piston: Valve V is open. V is closed, The gas to which heat energy has been added in the Heater (Heat source) increasing its pressure now expands.

b. in the space below the piston: Valve V is closed. Valve V is open. The cool gas sucked in during the previous stroke is compressed and displaced into the Heater through the Regenerator.

' The intended processes for the working medium can now be traced as follows: Starting at its lowest temperature at the exit of the Cooler, the working medium is sucked into the space below the piston. It is then compressed (adiabatically) and admitted to the Heater through the Regenerator. In the Regenerator, the working medium picks up some heat energy (at constant pressure) and is then further heated (at constant volume) in the Heater to its maximum temperature and pres sure in the cycle. The time required for the entire upward stroke of the piston is available for heat transfer to the working medium in the Heater. This process is intended to take place at constant volume by keeping the valves V and V, shut. The working medium is now made to expand (adiabatically) in the space above the piston such that its pressure falls down to the lowest pressure in the cycle. This is achieved by providing a higher volume ratio during expansion than that during compression. These ratios can be adjusted to the appropriate values by choosing the correct piston rod diameter.

The. working medium is then displaced into the. Cooler through the Regenerator which picks up a part of the heat energy (at constant pressure) remaining in the working medium. The working medium is finally cooled to its lowest temperature in the cycle in the Cooler (at constant pressure). This completes the thermodynamic cycle of the working medium.

The ideal thermodynamic cycle for the working medium is shown in FIG. 7. The following points should be noted in connection with this engine.

a. The expansion ratio is higher than the compression ratio. This results in the utilization of the toe of the indicator diagram that is nonnally lost in conventional engines where the compression and expansion ratios are nearly equal. It is possible to achieve this because the compression and the expansion processes take place on opposite sides of the piston in the present engine.

b. The process of regeneration at the end of the compression process (at low compression ratios), utilizes some of the energy in the gases that have undergone expansion. This raises the mean temperature at which heat is added and lowers the mean temperature at which heat is rejected in the cycle.

c. The process of heat addition takes place essentially at constant volume in the time interval required for the entire upward stroke of the piston.

As is well known, all these factors contribute to a high thermal efficiency of the thermodynamic cycle. It is however true that the entire working medium may not execute the ideal thermodynamic cycle shown in FIG. 7. In addition, there are the inevitable losses due to component imperfections. Nevertheless, it is possible that the Relative Efficiency (Actual Efficiency/Ideal Efficiency) of this engine would be comparable to that achieved by the Philips Stirling Engine in view of its comparatively simple mechanical layout.

A detailed analysis of this thermodynamic cycle has been carried out using a digital computer. The maximum cycle temperature was fixed at 600 C. l,570 R.) as specified. The following gases were investigated in turn as to their performance as working media in the engine: Air, Nitrogen, Carbon Dioxide, Hydrogen Helium, Argon, Sulphur Dioxide. Air and Carbon Dioxide result in a better performance than the rest with Carbon Dioxide giving the best overall performance.

The results obtained on the computer with Carbon Dioxide and Air as working media are plotted in FIGS. 8 and 9 respectively. The process of regeneration can be effected only as long as the temperature at the end of the compression process is lower than the temperature at the end of the expansion process. Curves A and B in FIGS. 8 and 9 therefore merge with each other at some value of the compression ratio. Curve C in FIGS. 8 and 9 shows the specific output of the engine the output per unit rate of mass flow of the working medium through the engine. Thus, for a given output, there are two ways of keeping the dimensions of the engine to any desired value:

a. Varying the engine speed. b. Varying the mean pressure and hence the mean density of the working medium in the engine.

A practical limitation on the minimum size of the engine may be imposed by the speed being limited by the rate of heat transfer in the regenerator. Also, the minimum mean pressure may be determined by heat transfer.

An analytical expression for the thermal efficiency of the ideal cycle is derived in Appendix A. Some approximate perfon'nance calculations of a Carbon dioxide engine for the present application are shown in Appendix B.

These preliminary performance calculations indicate that the new heat engine concept presented herein does indeed show great potential as a prime mover for many applications and warrants further investigation and development work. In

. addition to a high thermal efficiency, the following advantages may also accrue:

Referring to FIG. 7, which shows the ideal thermodynamic cycle of the engine, assume unit mass of working medium. In the ideal cycle, the regenerator has an efficiency of percent.

Now.

Where CR Compression Ratio. 'y Ratio of specific heats. C IC Thermal Efficiency= 1 Heat refined This relation expresses the thermal efficiency of the Cycle in terms of the Compression Ratio, the maximum Cycle temperature T and the minimum Cycle temperature T,.

APPENDIX B Carbon dioxide Engine: Compression Ratio 3 Expansion Ration 4.1 Thermal Efficiency: 50.9 [FIG. 8] Specific Output 44,159 Watts/lbm per sec. [FIG 8] Relative Efficiency: 60% (assume) Generator Efficiency 85% (assume) Overall Conversion Efficiency 50.9 X 0.6 X 0.85 =26% Actual Output desired 600 W ldeal indicated output (600) (0.6 X 0.85) 1,175W Molecular Weight of Carbon dioxide 44.01 Density of Carbon dioxide at 540 R. and 14.5 psia 14.5 X 144 X 44.01 (1,545 X 540)=0.11lbm/cft :Volume flow through engine per sec. (1,175) (44,159 X 0.11)= 0.242 cft/sec Assume engine rpm 1,000 Displacement in suction chamber per stroke (0.242 X 60 x 1,728) 1,000) =25.l inch Assuming a stroke/bore ratio for engine of l .0,

(77'0") (4) 25.1 Where D Cylinder diameter D a 3.17 inches Length of working Cylinder 7 inches The engine can be made more compact, if desired, by increasing the engine rpm and/or increasing the mean pressure of carbon dioxide in the engine.

1 claim 1. A method of converting energy, available in a thermal source, into mechanical energy in a continuous closed cycle sequence utilizing a working medium which is at all times gaseous, said method comprising the steps:

i. compressing the said working medium in a first space having a lower mean temperature and pressure by a compression ratio r, i

ii. adding heat H. at substantially constant pressure to the compressed medium,

iii. adding further heat H, from the said source to the compressed medium at substantially constant volume,

iv. expanding the said medium into a second space having a higher mean temperature and pressure by an expansion ratio R, where R is numerically greater than r,

v. extracting an amount of heat nominally equivalent to P1,,

from the expanded medium at substantially constant pressure, said amount of heat H providing that heat required in step (ii),

vi. cooling said medium at substantially constant pressure,

and,

vii. utilizing the work done by the medium during the expansion step (iv) to provide firstly, that work required for the compression step (i) and secondly, a mechanical output, and

viii. cyclically repeating steps (i) to (vii).

2. A method as claimed in claim 1, wherein said compression and expansion steps are nominally adiabatic.

3. A method as claimed in claim 1 wherein said first and second spaces together form a fixed volume, the respective spaces being separated by a movable member within said fixed volume and wherein the net force acting on the said movable member at any time is due to pressures acting upon opposite sides thereof.

4. Apparatus for the conversion of energy available in a thermal source into mechanical energy using a gaseous working medium said apparatus comprising in succession:

i. compression means for nominally adiabatic compression of the said working medium by a compression ratio r,

ii. heat exchanger output means for adding heat at substantially constant pressures to the compressed medium,

iii. means for adding further heat at substantially constant volume to the compressed medium,

iv. expansion means for nominally adiabatic expansion of the said compressed and heated medium through an expansion ratio R where R is numerically greater than r,

v. means connecting items (iv) and (i) to divert a first portion of the energy converted in the expansion means to drive said compression means,

vi. heat exchanger input means operatively associated with the said heat exchanger output means for extracting heat at substantially constant pressure from the expanded medium and for providing the added heat in step (ii),

cooling means for extracting further heat at substantially constant pressure from the expanded medium,

viii. means to divert a second portion of the energy converted in the expansion means to a mechanical output, and,

ix. means for repeatively cycling items (i) to (viii) in succession.

5. Apparatus as claimed in claim 4 wherein items (i) and (iv) are further comprising piston and cylinder means.

6. Apparatus as claimed in claim 5 wherein there is a single cylinder and piston common to items (i) and (iv), said cylinder including inlet and outlet valves.

7. Apparatus as claimed in claim 6 wherein said piston includes a piston rod constituting said mechanical output. 

1. A method of converting energy, available in a thermal source, into mechanical energy in a continuous closed cycle sequence utilizing a working medium which is at all times gaseous, said method comprising the steps: i. compressing the said working medium in a first space having a lower mean temperature and pressure by a compression ratio ''r'', ii. adding heat Hr at substantially constant pressure to the compressed medium, iii. adding further heat Hs from the said source to the compressed medium at substantially constant volume, iv. expanding the said medium into a second space having a higher mean temperature and pressure by an expansion ratio ''R'', where R is numerically greater than r, v. extracting an amount of heat nominally equivalent to Hr, from the expanded medium at substantially constant pressure, said amount of heat Hr providing that heat required in step (ii), vi. cooling said medium at substantially constant pressure, and, vii. utilizing the work done by the medium during the expansion step (iv) to provide firstly, that work required for the compression step (i) and secondly, a mechanical output, and viii. cyclically repeating steps (i) to (vii).
 2. A method as claimed in claim 1, wherein said compression and expansion steps are nominally adiabatic.
 3. A method as claimed in claim 1 wherein said first and second spaces together form a fixed volume, the respective spaces being separated by a movable member within said fixed volume and wherein the net force acting on the said movable member at any time is due to pressures acting upon opposite sides thereof.
 4. Apparatus for the conversion of energy available in a thermal source into mechanical energy using a gaseous working medium said apparatus comprising in succession: i. compression means for nominally adiabatic compression of the said working medium by a compression ratio ''r'', ii. heat exchanger output means for adding heat at substantially constant pressures to the compressed medium, iii. means for adding further heat at substantially constant volume to the compressed medium, iv. expansion means for nominally adiabatic expansion of the said compressed and heated medium through an expansion ratio ''R'' where R is numerically greater than r, v. means connecting items (iv) and (i) to divert a first portion of the energy converted in the expansion means to drive said compression means, vi. heat exchanger input means operatively associated with the said heat exchanger output means for extracting heaT at substantially constant pressure from the expanded medium and for providing the added heat in step (ii), vii. cooling means for extracting further heat at substantially constant pressure from the expanded medium, viii. means to divert a second portion of the energy converted in the expansion means to a mechanical output, and, ix. means for repeatively cycling items (i) to (viii) in succession.
 5. Apparatus as claimed in claim 4 wherein items (i) and (iv) are further comprising piston and cylinder means.
 6. Apparatus as claimed in claim 5 wherein there is a single cylinder and piston common to items (i) and (iv), said cylinder including inlet and outlet valves.
 7. Apparatus as claimed in claim 6 wherein said piston includes a piston rod constituting said mechanical output. 